Question 515509
Let x be the amount of money Samantha invested in Bank A, and let y be the amount she invested in Bank B.  The total amount of money she invested in the two banks was $10000, and we can represent this as an algebraic equation as:

x + y = 10000

Since Bank A paid 8% interest, she earned 0.08x in interest at Bank A.  Likewise, since Bank B paid 7% interest, she earned 0.07y at Bank B.  The total amount of interest she earned at the two banks was $735, and we can represent this fact as an algebraic equation as:

0.08x + 0.07y = 735

Now we have a system of two linear equations in two unknowns.  We can solve this system using the substitution method.  First, we will take the first equation and solve for x:

x + y = 10000
x = 10000 - y (subtracting y from both sides)

Now we substitute 10000 - y for x in the second equation, yielding an equation involving y only:

0.08(10000 - y) + 0.07y = 735

Now we solve for y:

800 - 0.08y + 0.07y = 735 (distributing 0.08 in the left side)
800 - 0.01y = 735 (combining like terms)
-0.01y = -65 (subtracting 800 from both sides)
y = 6500 (dividing both sides by -0.01)

So Samantha invested $6500 in Bank B, as you figured out intuitively.  Substituting 6500 back in for y in our equation for x, we then get:

x = 10000 - y = 10000 - 6500 = 3500

so, as you also figured out, she invested $3500 in Bank A.